I powered the board means connector (J1) with 13V DC On the first day worked. Uploaded a blink skecth.

The second day I do the same thing. But the power supply indicates a short circuit . With a tester I measured the entrance of j1 and in effect is short-circuited .

I followed the instructions : "When power is applied to J1 or VIN , the external power must be in the range of 7 to 17 V". With USB work but, thoroughly tested and cost that I can not load the sketch from the USB port J6 .

My suggestion for troubleshooting: make sure the lab supply is set for high enough current limit. It could be that the Edison draws too much current at startup, so the lab supply voltage sags. this causes the Edison to draw more current, because it contains a switching supply. I would crank up the lab supply to 3A to make sure the startup problem is not caused by the lab supply going into current limit.

Lab power supplies can have different characteristics. Some may have current foldback which can cause trouble when powering a switching converter. so I would recommend a different power supply before declaring the Edison U1 converter dead.

One thing to look out for is that the U1 power converter only has a small ceramic capacitor on the input. If you plug in a power supply into J1 using long wires there will be a voltage ringing across the 10uF ceramic capacitor, because the long wires can have significant inductance, especially if they are separate wires and not a cable. The LC circuit that is formed by this wire inductance and the ceramic capacitor can cause the capacitor voltage to briefly increase to twice the dc supply voltage. I am not familiar with the controller U1, but it has a maximum rating of 20V. It is theoretically possible at least, to exceed this voltage at plug in.

For what it is worth, I did notice that the LED for the LiPo charger was blinking in your case. I've never attached a battery to mine, and thus have never seen this LED lit. Perhaps there is something wrong with that part of the circuit? J2 is for attaching single cell lithium battery, and luckily I did not see a jumper there. I would expect that if the charging circuit saw a load there, it might start charging. With the device powered down and unplugged, I measured about 2.9Meg ohms across this jumper in one direction, and almost 7Meg in the opposite direction. If you are seeing a much lower resistance across these pins when the device is powered off, there might be an issue with the charging circuit.

As for what intel is willing to do to remedy this problem in your case, I cannot say.